score-trajectory-analysis

Research

Collect historical scores, fit saturation curves, detect inflection points

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Score Trajectory Analysis Tactic

Collect historical SOTA scores for a benchmark, arrange as time-series, fit saturation curves, and detect inflection points indicating phase transitions in benchmark difficulty.

Stages

Stage 1: Multi-Source Score Collection

Gather historical scores from multiple sources to build comprehensive timeline.

Sources (search in order):

Papers With Code leaderboards (primary)
Official benchmark leaderboards/websites
Individual papers reporting SOTA (via dare-ss, dare-scholar)
Blog posts and technical reports (via brave-search, dare-web)

Per data point, collect:

Model name and family
Score (primary metric)
Date (publication/release date)
Paper/source reference
Model size (parameters) if available
Training data scale if available

Minimum: 10 data points spanning at least 2 years.

Stage 2: Time-Series Arrangement

Sort by date
Compute SOTA envelope (monotonically non-decreasing maximum)
Identify score jumps > 2 standard deviations
Note human baseline and theoretical ceiling positions
Flag suspicious entries (unreplicated claims, withdrawn papers)

Stage 3: Curve Fitting

Fit multiple saturation models to the SOTA envelope:

Logistic: S(t) = L / (1 + e^(-k(t-t0)))
Exponential decay to ceiling: S(t) = C - (C-S0) * e^(-lambda*t)
Linear (for pre-saturation benchmarks)
Piecewise (for benchmarks with phase transitions)

Report goodness-of-fit (R-squared) for each model. Select best-fit.

Stage 4: Saturation/Inflection Detection

Classify benchmark status:

Pre-saturation: Linear or early logistic, >20% headroom remaining
Approaching: Mid-logistic, 5-20% headroom, decelerating gains
Saturated: <5% headroom, gains < noise level
Supersaturated: Multiple models at ceiling, benchmark no longer discriminative

Detect inflection points:

Acceleration phases (new paradigm unlocks rapid progress)
Deceleration phases (diminishing returns begin)
Step functions (single breakthrough causes discontinuous jump)

Output

trajectory:
  benchmark: string
  metric: string
  data_points: int
  time_span: string
  sota_envelope:
    - {date, score, model, source}
  best_fit_model: logistic|exponential|linear|piecewise
  fit_r_squared: float
  saturation_status: pre-saturation|approaching|saturated|supersaturated
  headroom: float
  inflection_points:
    - {date, type: acceleration|deceleration|step, cause: string}
  estimated_ceiling: float
  time_to_ceiling: string

Yield Report

Metric	Minimum
Data points collected	10
Sources consulted	3
Curve models fitted	3
Saturation classification produced	1